Revert "LinearAlgebra Function Added"

1 files changed, 293 insertions, 0 deletions

diff --git a/2.3-1/thirdparty/includes/GSL/gsl/gsl_sf_gamma.h b/2.3-1/thirdparty/includes/GSL/gsl/gsl_sf_gamma.h
new file mode 100644
index 00000000..d5e867ba
--- /dev/null
+++ b/2.3-1/thirdparty/includes/GSL/gsl/gsl_sf_gamma.h
@@ -0,0 +1,293 @@
+/* specfunc/gsl_sf_gamma.h
+ * 
+ * Copyright (C) 1996, 1997, 1998, 1999, 2000 Gerard Jungman
+ * 
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 3 of the License, or (at
+ * your option) any later version.
+ * 
+ * This program is distributed in the hope that it will be useful, but
+ * WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+ * General Public License for more details.
+ * 
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
+ */
+
+/* Author:  G. Jungman */
+
+#ifndef __GSL_SF_GAMMA_H__
+#define __GSL_SF_GAMMA_H__
+
+#include <gsl/gsl_sf_result.h>
+
+#undef __BEGIN_DECLS
+#undef __END_DECLS
+#ifdef __cplusplus
+# define __BEGIN_DECLS extern "C" {
+# define __END_DECLS }
+#else
+# define __BEGIN_DECLS /* empty */
+# define __END_DECLS /* empty */
+#endif
+
+__BEGIN_DECLS
+
+
+/* Log[Gamma(x)], x not a negative integer
+ * Uses real Lanczos method.
+ * Returns the real part of Log[Gamma[x]] when x < 0,
+ * i.e. Log[|Gamma[x]|].
+ *
+ * exceptions: GSL_EDOM, GSL_EROUND
+ */
+int gsl_sf_lngamma_e(double x, gsl_sf_result * result);
+double gsl_sf_lngamma(const double x);
+
+
+/* Log[Gamma(x)], x not a negative integer
+ * Uses real Lanczos method. Determines
+ * the sign of Gamma[x] as well as Log[|Gamma[x]|] for x < 0.
+ * So Gamma[x] = sgn * Exp[result_lg].
+ *
+ * exceptions: GSL_EDOM, GSL_EROUND
+ */
+int gsl_sf_lngamma_sgn_e(double x, gsl_sf_result * result_lg, double *sgn);
+
+
+/* Gamma(x), x not a negative integer
+ * Uses real Lanczos method.
+ *
+ * exceptions: GSL_EDOM, GSL_EOVRFLW, GSL_EROUND
+ */
+int gsl_sf_gamma_e(const double x, gsl_sf_result * result);
+double gsl_sf_gamma(const double x);
+
+
+/* Regulated Gamma Function, x > 0
+ * Gamma^*(x) = Gamma(x)/(Sqrt[2Pi] x^(x-1/2) exp(-x))
+ *            = (1 + 1/(12x) + ...),  x->Inf
+ * A useful suggestion of Temme.
+ *
+ * exceptions: GSL_EDOM
+ */
+int gsl_sf_gammastar_e(const double x, gsl_sf_result * result);
+double gsl_sf_gammastar(const double x);
+
+
+/* 1/Gamma(x)
+ * Uses real Lanczos method.
+ *
+ * exceptions: GSL_EUNDRFLW, GSL_EROUND
+ */
+int gsl_sf_gammainv_e(const double x, gsl_sf_result * result);
+double gsl_sf_gammainv(const double x);
+
+
+/* Log[Gamma(z)] for z complex, z not a negative integer
+ * Uses complex Lanczos method. Note that the phase part (arg)
+ * is not well-determined when |z| is very large, due
+ * to inevitable roundoff in restricting to (-Pi,Pi].
+ * This will raise the GSL_ELOSS exception when it occurs.
+ * The absolute value part (lnr), however, never suffers.
+ *
+ * Calculates:
+ *   lnr = log|Gamma(z)|
+ *   arg = arg(Gamma(z))  in (-Pi, Pi]
+ *
+ * exceptions: GSL_EDOM, GSL_ELOSS
+ */
+int gsl_sf_lngamma_complex_e(double zr, double zi, gsl_sf_result * lnr, gsl_sf_result * arg);
+
+
+/* x^n / n!
+ *
+ * x >= 0.0, n >= 0
+ * exceptions: GSL_EDOM, GSL_EOVRFLW, GSL_EUNDRFLW
+ */
+int gsl_sf_taylorcoeff_e(const int n, const double x, gsl_sf_result * result);
+double gsl_sf_taylorcoeff(const int n, const double x);
+
+
+/* n!
+ *
+ * exceptions: GSL_EDOM, GSL_EOVRFLW
+ */
+int gsl_sf_fact_e(const unsigned int n, gsl_sf_result * result);
+double gsl_sf_fact(const unsigned int n);
+
+
+/* n!! = n(n-2)(n-4) ... 
+ *
+ * exceptions: GSL_EDOM, GSL_EOVRFLW
+ */
+int gsl_sf_doublefact_e(const unsigned int n, gsl_sf_result * result);
+double gsl_sf_doublefact(const unsigned int n);
+
+
+/* log(n!) 
+ * Faster than ln(Gamma(n+1)) for n < 170; defers for larger n.
+ *
+ * exceptions: none
+ */
+int gsl_sf_lnfact_e(const unsigned int n, gsl_sf_result * result);
+double gsl_sf_lnfact(const unsigned int n);
+
+
+/* log(n!!) 
+ *
+ * exceptions: none
+ */
+int gsl_sf_lndoublefact_e(const unsigned int n, gsl_sf_result * result);
+double gsl_sf_lndoublefact(const unsigned int n);
+
+
+/* log(n choose m)
+ *
+ * exceptions: GSL_EDOM 
+ */
+int gsl_sf_lnchoose_e(unsigned int n, unsigned int m, gsl_sf_result * result);
+double gsl_sf_lnchoose(unsigned int n, unsigned int m);
+
+
+/* n choose m
+ *
+ * exceptions: GSL_EDOM, GSL_EOVRFLW
+ */
+int gsl_sf_choose_e(unsigned int n, unsigned int m, gsl_sf_result * result);
+double gsl_sf_choose(unsigned int n, unsigned int m);
+
+
+/* Logarithm of Pochhammer (Apell) symbol
+ *   log( (a)_x )
+ *   where (a)_x := Gamma[a + x]/Gamma[a]
+ *
+ * a > 0, a+x > 0
+ *
+ * exceptions:  GSL_EDOM
+ */
+int gsl_sf_lnpoch_e(const double a, const double x, gsl_sf_result * result);
+double gsl_sf_lnpoch(const double a, const double x);
+
+
+/* Logarithm of Pochhammer (Apell) symbol, with sign information.
+ *   result = log( |(a)_x| )
+ *   sgn    = sgn( (a)_x )
+ *   where (a)_x := Gamma[a + x]/Gamma[a]
+ *
+ * a != neg integer, a+x != neg integer
+ *
+ * exceptions:  GSL_EDOM
+ */
+int gsl_sf_lnpoch_sgn_e(const double a, const double x, gsl_sf_result * result, double * sgn);
+
+
+/* Pochhammer (Apell) symbol
+ *   (a)_x := Gamma[a + x]/Gamma[x]
+ *
+ * a != neg integer, a+x != neg integer
+ *
+ * exceptions:  GSL_EDOM, GSL_EOVRFLW
+ */
+int gsl_sf_poch_e(const double a, const double x, gsl_sf_result * result);
+double gsl_sf_poch(const double a, const double x);
+
+
+/* Relative Pochhammer (Apell) symbol
+ *   ((a,x) - 1)/x
+ *   where (a,x) = (a)_x := Gamma[a + x]/Gamma[a]
+ *
+ * exceptions:  GSL_EDOM
+ */
+int gsl_sf_pochrel_e(const double a, const double x, gsl_sf_result * result);
+double gsl_sf_pochrel(const double a, const double x);
+
+
+/* Normalized Incomplete Gamma Function
+ *
+ * Q(a,x) = 1/Gamma(a) Integral[ t^(a-1) e^(-t), {t,x,Infinity} ]
+ *
+ * a >= 0, x >= 0
+ *   Q(a,0) := 1
+ *   Q(0,x) := 0, x != 0
+ *
+ * exceptions: GSL_EDOM
+ */
+int gsl_sf_gamma_inc_Q_e(const double a, const double x, gsl_sf_result * result);
+double gsl_sf_gamma_inc_Q(const double a, const double x);
+
+
+/* Complementary Normalized Incomplete Gamma Function
+ *
+ * P(a,x) = 1/Gamma(a) Integral[ t^(a-1) e^(-t), {t,0,x} ]
+ *
+ * a > 0, x >= 0
+ *
+ * exceptions: GSL_EDOM
+ */
+int gsl_sf_gamma_inc_P_e(const double a, const double x, gsl_sf_result * result);
+double gsl_sf_gamma_inc_P(const double a, const double x);
+
+
+/* Non-normalized Incomplete Gamma Function
+ *
+ * Gamma(a,x) := Integral[ t^(a-1) e^(-t), {t,x,Infinity} ]
+ *
+ * x >= 0.0
+ *   Gamma(a, 0) := Gamma(a)
+ *
+ * exceptions: GSL_EDOM
+ */
+int gsl_sf_gamma_inc_e(const double a, const double x, gsl_sf_result * result);
+double gsl_sf_gamma_inc(const double a, const double x);
+
+
+/* Logarithm of Beta Function
+ * Log[B(a,b)]
+ *
+ * a > 0, b > 0
+ * exceptions: GSL_EDOM
+ */
+int gsl_sf_lnbeta_e(const double a, const double b, gsl_sf_result * result);
+double gsl_sf_lnbeta(const double a, const double b);
+
+int gsl_sf_lnbeta_sgn_e(const double x, const double y, gsl_sf_result * result, double * sgn);
+
+
+/* Beta Function
+ * B(a,b)
+ *
+ * a > 0, b > 0
+ * exceptions: GSL_EDOM, GSL_EOVRFLW, GSL_EUNDRFLW
+ */
+int gsl_sf_beta_e(const double a, const double b, gsl_sf_result * result);
+double gsl_sf_beta(const double a, const double b);
+
+
+/* Normalized Incomplete Beta Function
+ * B_x(a,b)/B(a,b)
+ *
+ * a > 0, b > 0, 0 <= x <= 1
+ * exceptions: GSL_EDOM, GSL_EUNDRFLW
+ */
+int gsl_sf_beta_inc_e(const double a, const double b, const double x, gsl_sf_result * result);
+double gsl_sf_beta_inc(const double a, const double b, const double x);
+
+
+/* The maximum x such that gamma(x) is not
+ * considered an overflow.
+ */
+#define GSL_SF_GAMMA_XMAX  171.0
+
+/* The maximum n such that gsl_sf_fact(n) does not give an overflow. */
+#define GSL_SF_FACT_NMAX 170
+
+/* The maximum n such that gsl_sf_doublefact(n) does not give an overflow. */
+#define GSL_SF_DOUBLEFACT_NMAX 297
+
+__END_DECLS
+
+#endif /* __GSL_SF_GAMMA_H__ */